Breadth First Search or BFS for a Graph traversal
- 1. Objectives ▪ To understand the concept of BFS Traversal ▪ How to use BFS Traversal in solving the real world problems
- 2. Breadth First Search Traversal(BFS) ▪ BFS traversal of a graph produces a spanning tree as final result. ▪ Spanning Tree is a graph without loops. ▪ We use Queue data structure with maximum size of total number of vertices in the graph to implement BFS traversal.
- 3. Steps to implement BFS Traversal ▪ Step 1 - Define a Queue of size total number of vertices in the graph. ▪ Step 2 - Select any vertex as starting point for traversal. Visit that vertex and insert it into the Queue. ▪ Step 3 - Visit all the non-visited adjacent vertices of the vertex which is at front of the Queue and insert them into the Queue. ▪ Step 4 - When there is no new vertex to be visited from the vertex which is at front of the Queue then delete that vertex. ▪ Step 5 - Repeat steps 3 and 4 until queue becomes empty. ▪ Step 6 - When queue becomes empty, then produce final spanning tree by removing unused edges from the graph
- 4. Example Consider the following graph to perform BFS Traversal ◻Graph Traversals A B C D E F G
- 5. BFS Traversal ▪ Step-1:Select the vertex A as starting vertex(visit A) ▪Insert A into the Queue A B C D E F G Queue A
- 6. BFS Traversal ▪ Step-2:Visit the adjacent vertex of A which is not visited(D,E,B) ▪ Insert newly visited vertices into the Queue and delete A from the queue A B C D E F G Queue D E B
- 7. BFS Traversal ▪ Step-3:Visit all adjacent vertices of D which are not visited(there is no vertex) ▪ Delete D from the queue A B C D E F G Queue E B
- 8. BFS Traversal ▪ Step-4:Visit all the adjacent vertices of E which are not visited(C,F) ▪ Insert newly visited vertices into the Queue and delete E from the queue A B C D E F G Queue B C F
- 9. BFS Traversal ▪ Step-5:Visit all the adjacent vertices of B which are not visited(there is no vertex) ▪ Delete B from the queue A B C D E F G Queue C F
- 10. BFS Traversal ▪ Step-6:Visit all the adjacent vertices of C which are not visited(G) ▪ Insert newly visited vertex into the queue and delete C from the queue A B C D E F G Queue F G
- 11. BFS Traversal ▪ Step-7:Visit all the adjacent vertices of F which are not visited(there is no vertex) ▪ Delete F from the queue A B C D E F G Queue G
- 12. BFS Traversal ▪ Step-8:Visit all the adjacent vertices of G which are not visited(there is no vertex) ▪ Delete G from the queue A B C D E F G Queue
- 13. BFS Traversal ▪ Queue becomes empty.so,stop the process of BFS ▪ Final result of the spanning tree is shown below A B C D E F G
- 14. Thank you